Consider a manufacturing plant with the cost function C(q) =300 +100q - 4q^2 + 0

Question

Consider a manufacturing plant with the cost function

C(q) =300 +100q - 4q^2 + 0.2q^3

a) Identify the fixed cost and variable cost components of the cost function.
b) Derive the formulas for the firm’s average, average fixed, average variable, and marginal costs.
c) Draw two figures, one above the other. In the top figure, plot the total, variable, and fixed cost curves. In the bottom figure, show the average and marginal cost curves. Use Excel and plot for enough values of q between 0 and 20 such that the various curves are fairly smooth, say 40 0.5-increments between 0.5 and 20.0, inclusive.
d) On the bottom figure from part c), identify the points where marginal cost intersects average cost and average variable cost. This part may be answered by hand. What special feature characterises the corresponding points in the top figure? Consider rays from the origin to these points.

Explanation / Answer

a. fixed cost=300 variable cost VC=100q-4q*2+0.2q*3 b. average fixed cost 300/q average variable cost=VC/q=100-4q+0.2q*2 marginal cost=dTC/dq=100-8q+0.6q*2 c and d are yours.

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